ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 25 Feb 2021 18:55:17 +0100Differential forms and chain rulehttps://ask.sagemath.org/question/55909/differential-forms-and-chain-rule/Is there any way to use the chain rule on differential forms in Sage e.g. d(1/z) = -z^(-2)dz ?
From what I've understood in the reference manual, differential forms are defined via a manifold and coordinate charts which doesn't seem to allow it. I am working with forms that can be arbitrarily big, so I think it would be better for me to treat this as a purely algebraic object with no reference to any charts, but I guess this cannot be avoided ?
Sorry for the somewhat naive question, I am new to Sage.OvoctarThu, 25 Feb 2021 18:55:17 +0100https://ask.sagemath.org/question/55909/Can I express an abstract, symbolic range of reals?https://ask.sagemath.org/question/51935/can-i-express-an-abstract-symbolic-range-of-reals/Hello,
I'm very new at sage.
I'd like to express a range like range(-3.0,3.0,0.02) but with symbols for all the parameters, like range(a,b,delta), that displays nicely with show(). I would like to be able to substitute in floats at some later stage.
a. I'm not sure what a conventional symbolic expression for a range of floats is
b. Not sure how to express it in SageMath.
My goal is to be able to express constructing a chain rule over a finite input range. I seem to be able to express the chaining of functions ok, but am getting stuck with what i'm calling the constant function which is this range. If I use the range(-3.0,3.0,0.02) I get swamped by the output.
P.S. I don't want to use a built-in differentiate, I'm going to use finite differences.
Cheers...banksiaboySat, 13 Jun 2020 04:03:56 +0200https://ask.sagemath.org/question/51935/help on using chain rule in Sagehttps://ask.sagemath.org/question/36673/help-on-using-chain-rule-in-sage/Does anyone have any tips for using Sage to take derivatives of functions of many variables?
For example, if I define
```w(x,y) = x^2 + y^2``` (say)
and then if I suppose that ```x``` and ```y``` depend on an independent variable ```t```, the chain rule applies for finding ```w.diff(t)```. The only way I found to do this in Sage is
```var('t')```
```x(t) = cos(t)``` (say)
```y(t) = sin(t)```
```w(x,y) = x^2 + y^2```
```w.diff(t)```
But this isn't really using the chain rule. If I instead try
```var('x,y')```
```(define w again)```
```(define x and y again)```
```w.diff(t)```
```Out: (x,y) |--> 0```
Apparently it thinks the derivative is zero because it still thinks ```x``` and ```y``` are two independent variables where they appear in ```w```, even though you get
```x```
```Out: t |--> cos(t)```
and similarly for ```y```. Any suggestions? Thanks.
lefthandstanderMon, 20 Feb 2017 08:25:01 +0100https://ask.sagemath.org/question/36673/